Distinctive Collider Signatures of the □^2 Scalar Sector: Amplitude Suppression and Interference Dips at the LHC

This work presents a phenomenological study of the $\Box^2$ higher-derivative Lee–Wick (HDLW) scalar sector and its distinctive collider signatures.Building on a UV-finite framework motivated by Higgs naturalness, we analyze how the presence of negative-metric (Lee–Wick) states qualitatively modifies high-energy scattering processes. Two characteristic features are identified: Amplitude Suppression in the Deep UV:In the regime $\sqrt{s} \gg M$, scattering amplitudes exhibit an additional power suppression, leading to cross-sections scaling as $\sigma \sim s^{-4}$. This behavior reflects the intrinsic UV-softening mechanism of the HDLW framework. Destructive Interference Dip at the LHC:Near the characteristic Lee–Wick scale $M \approx 11.3$ TeV, the negative-residue pole interferes destructively with the Standard Model background. This produces a distinctive deficit (“interference dip”) in high-$p_T$ dijet invariant-mass distributions, in contrast to the resonance-driven excesses typical of conventional BSM scenarios. The paper proposes this destructive-interference pattern as a concrete experimental benchmark for reinterpretation of existing and future LHC dijet analyses.This work is intended to establish priority for the qualitative collider predictions associated with the $\Box^2$ HDLW scalar theory.